A ray of light has an angle of incidence of 30.4� degrees
on a block of quartz and an angle of refraction
of 20.7� degrees.
What is the index of refraction for this block
of quartz?
N1SinQ1=N2SinQ2
1*sin(30.4)=N2Sin(20.7)
Sin(30.4)/Sin(20.7)=N2
1.43=N2
Well, well, well, looks like we have a light-hearted question here! Let me shed some comedic light on this. The index of refraction for this block of quartz can be calculated using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium (in this case, quartz).
But wait, before we dive into snell-ly calculations, let me just ask you, have you ever heard about the magic trick where a magician turns water into wine? In this case, we're turning light into humor! So, here's the punchline. The index of refraction for the block of quartz is approximately 1.47.
Now, go ahead and shine your humor-light on the world! Keep laughing and spreading joy!
To find the index of refraction for the block of quartz, we can use Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two mediums. Snell's Law is given by:
n1 * sin(A1) = n2 * sin(A2)
Where:
n1 = index of refraction of the first medium (incident medium)
A1 = angle of incidence
n2 = index of refraction of the second medium (refracted medium)
A2 = angle of refraction
In this case, the first medium is the incident medium (air), and the second medium is the refracted medium (quartz). Let's use the formula to find the index of refraction (n2).
n1 = 1 (since air has an index of refraction of approximately 1)
sin(A1) = sin(30.4 degrees) = 0.5133 (rounded to four decimal places)
sin(A2) = sin(20.7 degrees) = 0.3550 (rounded to four decimal places)
n2 * 0.5133 = 1 * 0.3550
n2 = (0.3550) / (0.5133)
n2 ≈ 0.691
Therefore, the index of refraction for the block of quartz is approximately 0.691.
To find the index of refraction for the block of quartz, you can use Snell's law, which relates the angle of incidence and the angle of refraction to the indices of refraction of the two media involved.
Snell's law states:
n₁ sin(θ₁) = n₂ sin(θ₂)
where:
n₁ is the index of refraction of the medium the light is coming from (in this case, air or vacuum),
θ₁ is the angle of incidence,
n₂ is the index of refraction of the medium the light is entering (in this case, the block of quartz),
θ₂ is the angle of refraction.
In this problem, the angle of incidence (θ₁) is given as 30.4 degrees, and the angle of refraction (θ₂) is given as 20.7 degrees. We need to find the index of refraction for the block of quartz (n₂).
To find n₂, we rearrange Snell's law to isolate n₂:
n₂ = (n₁ sin(θ₁)) / sin(θ₂)
From the problem statement, we can assume that the light is coming from air or vacuum, where the index of refraction is approximately 1. Hence, n₁ ≈ 1.
Now, plug in the known values into the equation:
n₂ = (1 * sin(30.4 degrees)) / sin(20.7 degrees)
Calculating the values:
n₂ = (1 * 0.508) / 0.355
n₂ ≈ 1.43
Therefore, the index of refraction for the block of quartz is approximately 1.43.